# U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator

## Abstract

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.

- Authors:

- MS B283, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

- Publication Date:

- OSTI Identifier:
- 20699699

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 95; Journal Issue: 25; Other Information: DOI: 10.1103/PhysRevLett.95.252501; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; HARMONIC OSCILLATORS; POTENTIALS; RELATIVISTIC RANGE; SCALARS; SPIN; SYMMETRY; U-3 GROUPS; VECTORS

### Citation Formats

```
Ginocchio, Joseph N.
```*U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevLett.95.252501.

```
Ginocchio, Joseph N.
```*U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator*. United States. doi:10.1103/PhysRevLett.95.252501.

```
Ginocchio, Joseph N. Fri .
"U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator". United States.
doi:10.1103/PhysRevLett.95.252501.
```

```
@article{osti_20699699,
```

title = {U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator},

author = {Ginocchio, Joseph N.},

abstractNote = {We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.},

doi = {10.1103/PhysRevLett.95.252501},

journal = {Physical Review Letters},

number = 25,

volume = 95,

place = {United States},

year = {Fri Dec 16 00:00:00 EST 2005},

month = {Fri Dec 16 00:00:00 EST 2005}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.